More "words of wisdom" for my daughter ... and anyone else who may be interested. :-)
The other half of the equation, the "calories out" part, is as much a mistaken principle as the first. YES, to do work with the muscles "burns" an energy substrate -- either glucose or fatty acids. But to characterize the calories burned as the fat off our rumps is just wrong. Most of the energy burned by those sour-looking folks trotting down the street is glucose, from glycogen stored in their muscles and livers, which they promptly replenish from their diets full of hearthealthywholegrains. To burn fat as the primary fuel requires a low-carb diet and a specific kind of training.
So if they're not burning fat on their lengthy dawn jogs, why are they so skinny (or in many cases, skinny-fat)? Several reasons, like their high-carb lifestyles cause them to waste protein as described here; like they're not consuming enough or the right kind of calories to gain significant fat stores (the biggest "benefit" of a low-fat diet is that it's also low in omega-6s); or like they have the kind of bodies that are not prone to fattening in the first place.
The wrong kind of exercise has a big down-side, too. What Mark Sisson calls "chronic cardio" is notorious for promoting body-wide inflammation; ever hear about the theoretically-healthy young runners who drop dead of heart attacks, despite having little-to-no arterial plaque? THAT is the work of the inflammation. If you intrinsically LOVE running, it's bad enough because this kind of exercise is pretty stressful to the body; however, if you're only doing it because you think it's good for you and you basically dislike it, you're doubling-down on the stress hormones. And if you don't give your body time to recover from all the microtrauma (i.e., you run every day), the damage increases even more. The stress-hormone cortisol brings about all kinds of negative effects around the body, as well as increasing your tendency to fatten. You also experience more oxidative -- free-radical -- damage.
Then, the more you encourage the body to burn glucose, the worse it gets at burning fat. Nature is clever, and if it thinks you don't need the ability to do something, it will down-regulate production of the enzymes and other factors needed for it. Part of the process of becoming keto-adapted (able to burn fatty acids as one's primary fuel) is the adjustment of the body to producing all the chemicals needed to do it. If someone has burned glucose very largely for decades, the keto-adaptation period can be long and uncomfortable. The ability to switch between fuels easily is often called "metabolic flexibility" ... and it's a GOOD THING. ;-) Annoyingly, it's pretty easy for anyone to switch from fats to sugars, but not everybody swings the other way very well.
If exercise sucks for fat burning, why do most people -- even i -- think it's a good idea? Because moving around, flexing and relaxing your muscles, does a lot more than just burn energy. Exercise encourages your body to create more mitochondria -- the little power-stations that turn fuel into energy, vitality that allows one to enjoy life. You improve circulation, muscle strength and lung-power. You generate more natural growth hormone, and become more insulin-sensitive. The right kinds of exercise are relaxing and rejuvenating rather than stressful, especially if performed outside in pleasant surroundings or with pleasant company.
So yes, exercise can be a good thing, OR a bad thing depending on a bunch of variables ... like so many other things in life. Do something that you enjoy, which isn't damaging, and doesn't tense you up. Again borrowing from Mark S., the closer your workouts come to being PLAY, the better they are.
* okay, okay -- i've read "part deux" so many times, i had to play with the concept ... and everybody knows that 42 is a magical number. ;-) besides, since there's no "CICO is dead, part one" how COULD there be a part two?